{"title":"Lower order terms in the shape of cubic fields","authors":"Robert Hough, Eun Hye Lee","doi":"arxiv-2409.08417","DOIUrl":null,"url":null,"abstract":"We demonstrate equidistribution of the lattice shape of cubic fields when\nordered by discriminant, giving an estimate in the Eisenstein series spectrum\nwith a lower order main term. The analysis gives a separate discussion of the\ncontributions of reducible and irreducible binary cubic forms, following a\nmethod of Shintani. Our work answers a question posed at the American Institute\nof Math by giving a precise geometric and spectral description of an evident\nbarrier to equidistribution in the lattice shape.","PeriodicalId":501064,"journal":{"name":"arXiv - MATH - Number Theory","volume":"8 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Number Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08417","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We demonstrate equidistribution of the lattice shape of cubic fields when
ordered by discriminant, giving an estimate in the Eisenstein series spectrum
with a lower order main term. The analysis gives a separate discussion of the
contributions of reducible and irreducible binary cubic forms, following a
method of Shintani. Our work answers a question posed at the American Institute
of Math by giving a precise geometric and spectral description of an evident
barrier to equidistribution in the lattice shape.
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